The authors of [1]} start from a particular realization of the VA action imposed via a Langrange multiplier field \(T\)  that then becomes dynamical and ultimately leads to an instability. If that argument were to carry over to the anti-D3-brane and in particular to the anti-D3-brane uplift in the KKLT scenario, then one has to wonder whether it equally carries over to other scenarios as well: Four copies of the VA action arise from the worldvolume fermions on an anti-D3-brane on top of an O3-plane [2]}. If we remove the O3-plane, the fermionic action is unaltered [3]} and supplemented with a U(1) gauge field and three complex scalars. In flat space, however, there is no distinction between an anti-D3-brane and a D3-brane. This means these worldvolume fields on the brane form an \(\mathcal {N}=4\)  vector multiplet and the action is invariant under 16 linearly and 16 non-linearly realized supersymmetries. Clearly this supersymmetric system of an \(\mathcal {N}=4\)  vector multiplet is stable, although the action for the fermions is of VA type [3]}. Now let us do an O3 orientifold projection again but place the anti-D3-brane away from the orientifold (that maps it to a mirror anti-D3-brane). The action for this anti-D3-brane in flat space is exactly the same as the \(\mathcal {N}=4\)  vector multiplet action on the D3-brane. The orientifold background only projects out the 16 linear supersymmetries but it does not project out any of the fields on the anti-D3-brane. So, as is common in (intersecting) brane models in string theory, locally the amount of preserved supersymmetry is larger (\(\mathcal {N}=4\)  in 4d) than globally (\(\mathcal {N}=0\)  in this case). This simple thought experiment shows that it is nonsensical to conclude from the sheer presence of the VA action that a vacuum is unstable. The completion of the VA action through other fields leads for D3-branes and anti-D3-branes to locally supersymmetric actions. Any potential instability can only arise via the coupling to the background fields that requires a careful study and has been performed for the anti-D3-brane in the KKLT setup in the existing string theory literature, reaching the conclusion that the system is (meta-)stable.
